Answer
Verified
393.9k+ views
Hint: Find the area of the field by using formula for area of rectangle and find the area of the bed by using formula for area of square then subtract the area of both the squares from the area of the rectangle.
Complete step-by-step solution:
First, we will draw the figure to understand the question,
To obtain the area of the grass portion we have to subtract the area of flower beds from the area of land.
We are computing the area of land \[{A_l}\] by using the formula for area of rectangle \[A = l \cdot b\] where l is length and b is width.
Substituting \[l = 10.5\] and \[b = 4.2\] into \[A = l \cdot b\],
\[
{A_l} = 10.5 \times 4.2 \\
= 44.1{\text{ }}{{\text{m}}^2} \\
\]
Now we will compute the area of one bed by using the formula for area of square where a is the side of the square.
Substituting \[a = 1.2\] into \[A = {a^2}\],
\[
{A_b} = 1.2 \times 1.2 \\
= 1.44{\text{ }}{{\text{m}}^2} \\
\]
This is the area of one bed, multiplying \[{A_b}\] by two to find the area of both flower beds.
\[
2{A_b} = 2 \times 1.44 \\
= 2.88\,{{\text{m}}^2} \\
\]
Now, subtracting the area of both flower beds from the area of land,
\[
{A_l} - 2{A_b} = 44.1 - 2.88 \\
= 41.22{\text{ }}{{\text{m}}^2} \\
\]
Thus, the area of the grass portion of the field is \[41.22{\text{ }}{{\text{m}}^2}\].
Note:
In these types of questions find all the required areas, then subtract the smallest area from the largest area. The field has two square flower beds. Compute the area of one bed and multiply this area by two to get the area of both the beds.
Complete step-by-step solution:
First, we will draw the figure to understand the question,
To obtain the area of the grass portion we have to subtract the area of flower beds from the area of land.
We are computing the area of land \[{A_l}\] by using the formula for area of rectangle \[A = l \cdot b\] where l is length and b is width.
Substituting \[l = 10.5\] and \[b = 4.2\] into \[A = l \cdot b\],
\[
{A_l} = 10.5 \times 4.2 \\
= 44.1{\text{ }}{{\text{m}}^2} \\
\]
Now we will compute the area of one bed by using the formula for area of square where a is the side of the square.
Substituting \[a = 1.2\] into \[A = {a^2}\],
\[
{A_b} = 1.2 \times 1.2 \\
= 1.44{\text{ }}{{\text{m}}^2} \\
\]
This is the area of one bed, multiplying \[{A_b}\] by two to find the area of both flower beds.
\[
2{A_b} = 2 \times 1.44 \\
= 2.88\,{{\text{m}}^2} \\
\]
Now, subtracting the area of both flower beds from the area of land,
\[
{A_l} - 2{A_b} = 44.1 - 2.88 \\
= 41.22{\text{ }}{{\text{m}}^2} \\
\]
Thus, the area of the grass portion of the field is \[41.22{\text{ }}{{\text{m}}^2}\].
Note:
In these types of questions find all the required areas, then subtract the smallest area from the largest area. The field has two square flower beds. Compute the area of one bed and multiply this area by two to get the area of both the beds.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Which type of bond is stronger ionic or covalent class 12 chemistry CBSE
What organs are located on the left side of your body class 11 biology CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
How fast is 60 miles per hour in kilometres per ho class 10 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
When people say No pun intended what does that mea class 8 english CBSE